USING ANISOTROPIC DIFFUSION TO TRACK NEURAL FIBERS Sarah
USING ANISOTROPIC DIFFUSION TO TRACK NEURAL FIBERS Sarah Neyer NASA/JPL CSUN PAIR Advisor Dr. A. Alekseenko
Focus 1. This talk focuses on the brain scanning technique Diffusion Tensor Imaging 2. The problems they are facing with it 3. Our proposal of a solution 4. The two milestones of the project
What is the Problem? Problem: New imaging technique and we can’t use it! l l Meaning: Cannot assess the important data gathered about intricate fibers in brain l Proposal: New method to map these fibers
What is Diffusion Tensor Imaging? l New way to use Magnetic Resonance l Tracks H 2 O in the brain along fibers l Diseases it could diagnose l l ADHD Multiple Sclerosis
Tracking Fibers l Direction of fiber is known at every point l Connecting the directions is the problem l Where would this fiber go?
Current Method l Chooses between directions when it comes to them l Tracks one direction l It CANNOT track branching fibers
Proposed Method l Anisotropic Diffusion Equation l Looks at every direction at once! l It CAN account for branching fibers
First Step: Mimic diffusion l Ink drop on a piece of paper l Where it will diffuse comes from the brain scanning data
Second Step: Propagation 1. Anisotropic diffusion: Let it go anywhere 2. Isotropic diffusion: Sharpen the image
Third Step: Track the ridge l Ridge shows the fiber l Collect points based on highest curve l Eliminate the shape
Fourth Step: Repeat Diffusion l HUGE first drop VS small first drop l Smaller is better, more precision l We start a new drop where old one finishes
What the Fiber looks like! A 3 D view of straight fiber
Disadvantages l The algorithm takes too much time to complete l Why keep it? l It accounts for all points at once
What did we do? l Looked at the MATH behind diffusion l We made observations about behavior of diffusion l We came up with a faster algorithm
Ahhh… An Observation l l l We put random data in and observed After a long time we saw the structure of the fiber We realized that all we need is this solution, called the STATIC SOLUTION
Static Solution?
First step: Discretize the Equation l Discretizing means that we put in the data about how it acts in space and we can find how it acts in time l We studied the resulting ODEs in matrix form The discretized diffusion equation
Second Step: Analyze the Matrix Look at the Eigenvector corresponding to a zero Eigenvalue l An Eigenvalue, , is a number that scales a function with out changing its shape l Therefore a ZERO Eigenvalue gives the unchanged static solution l
Here’s what happened Circular fiber l Same l Time output! to create decreases!
Summary l We created an algorithm to find branching fibers using ANISOTROPIC DIFFUSION EQUATION l We looked at the Mathematics behind our equation l We found that we need the STATIC SOLUTION
Future Research l Use complicated brain data in research l Work on static solution to track ridge
Acknowledgements I would like to thank my advisor Dr. Alekseenko for working with me on this Project I would also like to thank the NASA/JPL PAIR Program for giving me this research opportunity
Questions?
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